Chapter 11: Q. 160E (page 1134)

In the following exercises, graph.
$\frac{{(x - 2)}^{2}}{4} - \frac{{(y - 3)}^{2}}{16} = 1$

Short Answer

Expert verified

The graph is as below

Step by step solution

Step 1. Given information

The equation is $\frac{{(x - 2)}^{2}}{4} - \frac{{(y - 3)}^{2}}{16} = 1$

Draw the graph.

Step 2. Calculation

The x² term is positive, the transverse axis is horizontal.

The hyperbola opens left and right.

Find the centre

Compare the equation with standard form $\frac{{(x - h)}^{2}}{a^{2}} - \frac{{(y - k)}^{2}}{b^{2}} = 1$

So, $(h, k) = (2, 3)$

$a^{2} = 4 \Rightarrow a = \pm 2$ and $b^{2} = 16 \Rightarrow b = \pm 4$

Sketch the rectangle that goes through the points 2 units left/right of centre 4 units above/ below the centre .

Step 3. Draw the graph

Sketch the asymptotes and draw the graph using asymptotes .

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In the following exercises, graph.
$\frac{{(x - 2)}^{2}}{4} - \frac{{(y - 3)}^{2}}{16} = 1$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

Step 3. Draw the graph

One App. One Place for Learning.

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In the following exercises, graph.x-224-y-3216=1

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculation

Step 3. Draw the graph

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

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Discrete Mathematics

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Study anywhere. Anytime. Across all devices.

In the following exercises, graph.
$\frac{{(x - 2)}^{2}}{4} - \frac{{(y - 3)}^{2}}{16} = 1$